Group #15696626 — subgroups

Subgroups — C₁₃×#10287 #15696626

Order 3328.

566 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3206	C₂	1	2	yes	maximal
2	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1962	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1548	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1276	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#532	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₁₃×#492	—	2	2	no	—
9	C₁₃×#487	—	2	2	no	—
10	C₁₃×#461	—	2	4	no	—
11	C₁₃×#448	—	2	4	no	—
12	C₁₃×#431	C₂²	1	2	yes	—
13	C₁₃×#423	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#104	—	2	2	no	—
15	C₁₃×#391	—	2	4	no	—
16	C₁₃×#382	—	2	2	no	—
17	C₄³×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#333	—	2	4	no	—
19	C₂×C₁₃×#41	—	2	1	no	—
20	C₂²×Q₈×C₁₃	D₄	1	4	yes	—
21	C₂×C₁₃×SD₁₆	—	2	8	no	—
22	C₂×C₁₃×M₁₆	—	2	1	no	—
23	C₁₃×C₄⋊Q₈	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
28	C₁₃×#127	D₄	1	1	yes	characteristic
29	C₁₃×#124	—	2	1	no	—
30	C₁₃×#121	—	2	2	no	—
31	C₄×D₄×C₁₃	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₄²×C₁₃	—	2	2	no	—
35	C₂×C₄²×C₁₃	D₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
39	C₁₃×#104	—	4	4	no	—
40	C₁₃×#103	—	2	8	no	—
41	C₁₃×C₂²⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₃	—	2	2	no	—
43	C₁₃×#95	—	2	8	no	—
44	#10287	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₁₃×#41	—	4	2	no	—
46	C₁₃×#41	—	4	2	no	—
47	C₂×Q₈×C₁₃	—	2	4	no	—
48	C₂×Q₈×C₁₃	—	2	1	no	—
49	C₂×Q₈×C₁₃	—	2	4	no	—
50	C₂×Q₈×C₁₃	—	4	8	no	—
51	C₂×D₄×C₁₃	—	2	2	no	—
52	C₂×D₄×C₁₃	—	2	1	no	—
53	C₂×D₄×C₁₃	—	4	1	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	—	2	4	no	—
56	C₂²×C₄×C₁₃	—	4	1	no	—
57	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₁₃×SD₁₆	—	8	8	no	—
60	C₁₃×M₁₆	—	4	2	no	—
61	C₂×C₈×C₁₃	—	2	4	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₁₃×C₄⋊C₄	—	4	2	no	—
68	C₁₃×C₂²⋊C₄	—	4	2	no	—
69	C₄²×C₁₃	—	2	2	no	—
70	C₄²×C₁₃	—	4	4	no	—
71	C₄²×C₁₃	SD₁₆	1	4	yes	complemented
72	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₃	C₂×D₄	1	2	yes	—
74	C₄²×C₁₃	#41	1	1	yes	characteristic
75	#3206	C₂×C₁₃	1	2	yes	—
76	#2862	C₂×C₁₃	1	1	yes	characteristic, complemented
77	#1962	C₂×C₁₃	1	1	yes	characteristic
78	#1548	C₂×C₁₃	1	2	yes	complemented
79	#1276	C₂×C₁₃	1	1	yes	characteristic, complemented
80	C₂³×C₁₃	—	4	1	no	—
81	C₂³×C₁₃	#120	1	1	yes	characteristic
82	Q₈×C₁₃	—	4	8	no	—
83	Q₈×C₁₃	—	4	2	no	—
84	Q₈×C₁₃	—	8	4	no	—
85	D₄×C₁₃	—	4	4	no	—
86	D₄×C₁₃	—	4	2	no	—
87	D₄×C₁₃	—	8	2	no	—
88	C₂×C₄×C₁₃	—	2	4	no	—
89	C₂×C₄×C₁₃	—	2	4	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	4	8	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	4	4	no	—
94	C₂×C₄×C₁₃	—	8	1	no	—
95	C₂×C₄×C₁₃	—	8	1	no	—
96	C₂×C₄×C₁₃	#120	1	2	yes	—
97	C₂×C₄×C₁₃	#121	1	2	yes	—
98	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
101	C₂×C₄×C₁₃	#137	1	2	yes	—
102	C₈×C₁₃	—	4	4	no	—
103	C₈×C₁₃	—	8	1	no	—
104	#532	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
106	#492	—	2	2	no	—
107	#487	—	2	2	no	—
108	#461	—	2	4	no	—
109	#448	—	2	4	no	—
110	#431	C₂²×C₁₃	1	2	yes	—
111	#423	C₂²×C₁₃	1	1	yes	characteristic
112	C₂×#104	—	2	2	no	—
113	#391	—	2	4	no	—
114	#382	—	2	2	no	—
115	C₄³	C₂²×C₁₃	1	1	yes	characteristic
116	#333	—	2	4	no	—
117	C₂²×C₁₃	—	2	2	no	—
118	C₂²×C₁₃	—	8	2	no	—
119	C₂²×C₁₃	—	8	1	no	—
120	C₂²×C₁₃	#392	1	1	yes	characteristic
121	C₂²×C₁₃	#448	1	2	yes	—
122	C₄×C₁₃	—	2	2	no	—
123	C₄×C₁₃	—	4	4	no	—
124	C₄×C₁₃	—	8	4	no	—
125	C₄×C₁₃	—	8	1	no	—
126	C₄×C₁₃	#455	1	4	yes	—
127	C₄×C₁₃	#461	1	2	yes	—
128	C₄×C₁₃	#492	1	1	yes	characteristic
129	C₄×C₁₃	#497	1	1	yes	characteristic
130	C₂×#41	—	2	1	no	—
131	C₂²×Q₈	D₄×C₁₃	1	4	yes	—
132	C₂×SD₁₆	—	2	8	no	—
133	C₂×M₁₆	—	2	1	no	—
134	C₄⋊Q₈	—	2	2	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	2	no	—
138	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
139	#127	D₄×C₁₃	1	1	yes	characteristic
140	#124	—	2	1	no	—
141	#121	—	2	2	no	—
142	C₄×D₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄²	—	2	2	no	—
146	C₂×C₄²	D₄×C₁₃	1	2	yes	—
147	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
148	C₄⋊C₈	—	2	2	no	—
149	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
150	#104	—	4	4	no	—
151	#103	—	2	8	no	—
152	C₂²⋊C₈	—	2	2	no	—
153	C₄×C₈	—	2	2	no	—
154	#95	—	2	8	no	—
155	C₂×C₁₃	—	2	2	no	—
156	C₂×C₁₃	—	16	1	no	—
157	C₂×C₁₃	#2004	1	2	yes	—
158	C₂×C₁₃	#2013	1	1	yes	characteristic
159	#41	—	4	2	no	—
160	#41	—	4	2	no	—
161	C₂×Q₈	—	2	4	no	—
162	C₂×Q₈	—	2	1	no	—
163	C₂×Q₈	—	2	4	no	—
164	C₂×Q₈	—	4	8	no	—
165	C₂×D₄	—	2	2	no	—
166	C₂×D₄	—	2	1	no	—
167	C₂×D₄	—	4	1	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	4	no	—
170	C₂²×C₄	—	4	1	no	—
171	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
172	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
173	SD₁₆	—	8	8	no	—
174	M₁₆	—	4	2	no	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	4	1	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₂²⋊C₄	—	4	2	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	4	4	no	—
185	C₄²	C₁₃×SD₁₆	1	4	yes	complemented
186	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
187	C₄²	C₂×D₄×C₁₃	1	2	yes	—
188	C₄²	C₁₃×#41	1	1	yes	characteristic
189	C₁₃	#10287	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³	—	4	1	no	—
191	C₂³	C₁₃×#120	1	1	yes	characteristic
192	Q₈	—	4	8	no	—
193	Q₈	—	4	2	no	—
194	Q₈	—	8	4	no	—
195	D₄	—	4	4	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	2	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	8	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	C₁₃×#120	1	2	yes	—
207	C₂×C₄	C₁₃×#121	1	2	yes	—
208	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
209	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
210	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
211	C₂×C₄	C₁₃×#137	1	2	yes	—
212	C₈	—	4	4	no	—
213	C₈	—	8	1	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	C₁₃×#392	1	1	yes	characteristic
218	C₂²	C₁₃×#448	1	2	yes	—
219	C₄	—	2	2	no	—
220	C₄	—	4	4	no	—
221	C₄	—	8	4	no	—
222	C₄	—	8	1	no	—
223	C₄	C₁₃×#455	1	4	yes	—
224	C₄	C₁₃×#461	1	2	yes	—
225	C₄	C₁₃×#492	1	1	yes	characteristic
226	C₄	C₁₃×#497	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	—	16	1	no	—
229	C₂	C₁₃×#2004	1	2	yes	—
230	C₂	C₁₃×#2013	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#3206

C₂

yes

maximal

C₁₃×#2862

C₂

yes

maximal, characteristic, complemented

C₁₃×#1962

C₂

yes

maximal, characteristic

C₁₃×#1548

C₂

yes

maximal, complemented

C₁₃×#1276

C₂

yes

maximal, characteristic, complemented

C₁₃×#532

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

—

C₁₃×#492

—

C₁₃×#487

—

C₁₃×#461

—

C₁₃×#448

—

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

characteristic

C₂×C₁₃×#104

—

C₁₃×#391

—

C₁₃×#382

—

C₄³×C₁₃

C₂²

yes

characteristic

C₁₃×#333

—

C₂×C₁₃×#41

—

C₂²×Q₈×C₁₃

D₄

yes

—

C₂×C₁₃×SD₁₆

—

C₂×C₁₃×M₁₆

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

D₄

yes

characteristic

C₁₃×#127

D₄

yes

characteristic

C₁₃×#124

—

C₁₃×#121

—

C₄×D₄×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

D₄

yes

—

C₁₃×#104

—

C₁₃×#103

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

#10287

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×SD₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

SD₁₆

yes

complemented

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

#3206

C₂×C₁₃

yes

—

#2862

C₂×C₁₃

yes

characteristic, complemented

#1962

C₂×C₁₃

yes

characteristic

#1548

C₂×C₁₃

yes

complemented

#1276

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

#120

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

100

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

101

C₂×C₄×C₁₃

#137

yes

—

102

C₈×C₁₃

—

103

C₈×C₁₃

—

104

#532

C₂²×C₁₃

yes

characteristic

105

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

—

106

#492

—

107

#487

—

108

#461

—

109

#448

—

110

#431

C₂²×C₁₃

yes

—

111

#423

C₂²×C₁₃

yes

characteristic

112

C₂×#104

—

113

#391

—

114

#382

—

115

C₄³

C₂²×C₁₃

yes

characteristic

116

#333

—

117

C₂²×C₁₃

—

118

C₂²×C₁₃

—

119

C₂²×C₁₃

—

120

C₂²×C₁₃

#392

yes

characteristic

121

C₂²×C₁₃

#448

yes

—

122

C₄×C₁₃

—

123

C₄×C₁₃

—

124

C₄×C₁₃

—

125

C₄×C₁₃

—

126

C₄×C₁₃

#455

yes

—

127

C₄×C₁₃

#461

yes

—

128

C₄×C₁₃

#492

yes

characteristic

129

C₄×C₁₃

#497

yes

characteristic

130

C₂×#41

—

131

C₂²×Q₈

D₄×C₁₃

yes

—

132

C₂×SD₁₆

—

133

C₂×M₁₆

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

D₄×C₁₃

yes

characteristic

139

#127

D₄×C₁₃

yes

characteristic

140

#124

—

141

#121

—

142

C₄×D₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄²

—

146

C₂×C₄²

D₄×C₁₃

yes

—

147

C₂×C₄²

C₂³×C₁₃

yes

characteristic

148

C₄⋊C₈

—

149

C₄⋊C₈

D₄×C₁₃

yes

—

150

#104

—

151

#103

—

152

C₂²⋊C₈

—

153

C₄×C₈

—

154

#95

—

155

C₂×C₁₃

—

156

C₂×C₁₃

—

157

C₂×C₁₃

#2004

yes

—

158

C₂×C₁₃

#2013

yes

characteristic

159

#41

—

160

#41

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂×D₄×C₁₃

yes

—

172

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

173

SD₁₆

—

174

M₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₂²⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

C₁₃×SD₁₆

yes

complemented

186

C₄²

C₂×D₄×C₁₃

yes

characteristic

187

C₄²

C₂×D₄×C₁₃

yes

—

188

C₄²

C₁₃×#41

yes

characteristic

189

C₁₃

#10287

yes

characteristic, direct product factor, Sylow

190

C₂³

—

191

C₂³

C₁₃×#120

yes

characteristic

192

Q₈

—

193

Q₈

—

194

Q₈

—

195

D₄

—

196

D₄

—

197

D₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₁₃×#120

yes

—

207

C₂×C₄

C₁₃×#121

yes

—

208

C₂×C₄

C₁₃×#121

yes

characteristic

209

C₂×C₄

C₁₃×#127

yes

characteristic

210

C₂×C₄

C₂×C₁₃×SD₁₆

yes

—

211

C₂×C₄

C₁₃×#137

yes

—

212

C₈

—

213

C₈

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₁₃×#392

yes

characteristic

218

C₂²

C₁₃×#448

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

C₁₃×#455

yes

—

224

C₄

C₁₃×#461

yes

—

225

C₄

C₁₃×#492

yes

characteristic

226

C₄

C₁₃×#497

yes

characteristic

227

C₂

—

228

C₂

—

229

C₂

C₁₃×#2004

yes

—

230

C₂

C₁₃×#2013

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₁₃×#532

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₁₃×#2862	C₂	semidirect
4. C₁₃×#1548	C₂	semidirect
5. C₁₃×#1276	C₂	semidirect
44. #10287	C₁₃	direct (N × H)
71. C₄²×C₁₃	SD₁₆	semidirect
76. #2862	C₂×C₁₃	semidirect
78. #1548	C₂×C₁₃	semidirect
79. #1276	C₂×C₁₃	semidirect
185. C₄²	C₁₃×SD₁₆	semidirect
189. C₁₃	#10287	direct (N × H)

H ≅ G/N

type

2. C₁₃×#2862

C₂

semidirect

4. C₁₃×#1548

C₂

semidirect

5. C₁₃×#1276

C₂

semidirect

44. #10287

C₁₃

direct (N × H)

71. C₄²×C₁₃

SD₁₆

semidirect

76. #2862

C₂×C₁₃

semidirect

78. #1548

C₂×C₁₃

semidirect

79. #1276

C₂×C₁₃

semidirect

185. C₄²

C₁₃×SD₁₆

semidirect

189. C₁₃

#10287

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3206	2
C₁₃×#2862	2
C₁₃×#1962	2
C₁₃×#1548	2
C₁₃×#1276	2
#10287	13

subgroup

index

C₁₃×#3206

C₁₃×#2862

C₁₃×#1962

C₁₃×#1548

C₁₃×#1276

#10287

Subgroups — C₁₃×#10287 #15696626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10287 #15696626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10287 #15696626